Difference between revisions of "L'Hôpital's Rule"
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==Problems== | ==Problems== | ||
===Introductory=== | ===Introductory=== | ||
| − | *Evaluate the limit <math>\lim_{x\rightarrow3}\frac{x^{2}-4x+3}{x^{2}-9}</math> ( | + | *Evaluate the limit <math>\lim_{x\rightarrow3}\frac{x^{2}-4x+3}{x^{2}-9}</math> ([[weblog_entry.php?t=168186 Source]]) |
| + | |||
===Intermediate=== | ===Intermediate=== | ||
===Olympiad=== | ===Olympiad=== | ||
Revision as of 13:35, 28 June 2021
L'Hopital's Rule is a theorem dealing with limits that is very important to calculus.
Theorem
The theorem states that for real functions 
, if 
![\[\lim\frac{f(x)}{g(x)}=\lim\frac{f'(x)}{g'(x)}\]](http://latex.artofproblemsolving.com/6/7/6/67664051ac365e271260749b981666330b2b71af.png)
Note that this implies that ![\[\lim\frac{f(x)}{g(x)}=\lim\frac{f^{(n)}(x)}{g^{(n)}(x)}=\lim\frac{f^{(-n)}(x)}{g^{(-n)}(x)}\]](http://latex.artofproblemsolving.com/f/6/6/f66ad9bb5b49e51afc1bf4dac34285dae981fd6f.png)
Proof
- No proof of this theorem is available at this time. You can help AoPSWiki by adding it.
Problems
Introductory
- Evaluate the limit
(weblog_entry.php?t=168186 Source)
(
